metric_const.cpp

/*
    Copyright 2017 Philippe Grandclement
 
    This file is part of Kadath.
 
    Kadath is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    Kadath is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with Kadath.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#include "space.hpp"
#include "tensor.hpp"
#include "metric.hpp"
#include "term_eq.hpp"
#include "scalar.hpp"
#include "tensor_impl.hpp"
#include "system_of_eqs.hpp"
#include "metric_tensor.hpp"
#include "name_tools.hpp"
namespace Kadath {
Metric_const::Metric_const (Metric_tensor& met) : 
        Metric_general(met) {
}
 
Metric_const::Metric_const (const Metric_const& so) :
        Metric_general (*so.p_met) {
}
 
Metric_const::~Metric_const() {
}
 
void Metric_const::set_system (System_of_eqs& ss, const char* name_met) {
 
    syst = &ss ;
 
    if (ss.met!=0x0) {
        cerr << "Metric already set for the system" << endl ;
        abort() ;
    }
 
    // Position in the system :
        place_syst = ss.ndom*ss.ncst ;
 
    ss.add_cst (0x0, *p_met) ;
 
    ss.met = this ;
    ss.name_met = new char[LMAX] ;
    trim_spaces (ss.name_met, name_met) ;
}
 
 
 
void Metric_const::compute_cov (int dd) const {
 
    int dim = espace.get_ndim() ;
    if (dim!=3) {
        cerr << "Function only implemented for dimension 3" << endl ;
        abort() ;
    }
 
    int place = place_syst + (dd-syst->dom_min) ;
 
    // Right storage : simple copy.
    if (type_tensor==COV) {
 
        if (p_met_cov[dd]==0x0)
            p_met_cov[dd] = new Term_eq(*syst->cst[place]) ;
        else
            *p_met_cov[dd] = Term_eq(*syst->cst[place]) ;
    }
    else {
        Term_eq** res = new Term_eq* [p_met->get_n_comp()] ;
        
        
        Scalar val (espace) ;
        Val_domain cmpval(espace.get_domain(dd)) ;
    
        Val_domain detval (espace.get_domain(dd)) ;
        detval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              + (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd)
              + (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              - (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)
              - (*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(1,1)(dd)
              - (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)  ;
 
        // Compo 1 1
        cmpval = (*syst->cst[place]->val_t)(2,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              -(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd) ;
        val.set_domain(dd) = cmpval / detval ;
        res[0] = new Term_eq (dd, val) ;
        
          
        // Compo 1 2
        cmpval = (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              -(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd) ;
        val.set_domain(dd) = cmpval / detval ;
        res[1] = new Term_eq (dd, val) ;
         
        // Compo 1 3
        cmpval = (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              -(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,2)(dd) ;
        val.set_domain(dd) = cmpval / detval ;
        res[2] = new Term_eq (dd, val) ;
        
        
        // Compo 2 2
        cmpval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              -(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd) ;
        val.set_domain(dd) = cmpval /detval ;
        res[3] = new Term_eq (dd, val) ;
        
        // Compo 2 3
        cmpval = (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)
              -(*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,3)(dd) ;
        val.set_domain(dd) = cmpval / detval ;
        res[4] = new Term_eq (dd, val) ;
        
        
          // Compo 3 3
        cmpval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)
              -(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(1,2)(dd) ;
        val.set_domain(dd) = cmpval /detval ;
        res[5] = new Term_eq (dd, val) ;
        
        
        // Value field :
        Metric_tensor resval (espace, COV, basis) ;
        resval.set(1,1) = res[0]->get_val_t() ;
        resval.set(1,2) = res[1]->get_val_t() ;
        resval.set(1,3) = res[2]->get_val_t() ;
        resval.set(2,2) = res[3]->get_val_t() ;
        resval.set(2,3) = res[4]->get_val_t() ;
        resval.set(3,3) = res[5]->get_val_t() ;
 
        Metric_tensor zero (espace, COV, basis) ;
        for (int i=1 ; i<=3 ; i++)
          for (int j=i ; j<=3 ; j++)
            zero.set(i,j) = 0 ;
        
        if (p_met_cov[dd]==0x0)
            p_met_cov[dd] = new Term_eq(dd, resval, zero) ;
        else
            *p_met_cov[dd] = Term_eq(dd, resval, zero) ;
        for (int i=0 ; i<p_met->get_n_comp() ; i++)
            delete res [i] ;
        delete [] res ;
    }
}
 
 
void Metric_const::compute_con (int dd) const {
    int dim = espace.get_ndim() ;
    if (dim!=3) {
        cerr << "Function only implemented for dimension 3" << endl ;
        abort() ;
    }
 
    int place = place_syst + (dd-syst->dom_min) ;
 
    // Right storage : simple copy.
    if (type_tensor==CON) {
 
        if (p_met_con[dd]==0x0)
            p_met_con[dd] = new Term_eq(*syst->cst[place]) ;
        else
            *p_met_con[dd] = Term_eq(*syst->cst[place]) ;
    }
    else {
      
        Term_eq** res = new Term_eq* [p_met->get_n_comp()] ;
        
        
        Scalar val (espace) ;
        Val_domain cmpval(espace.get_domain(dd)) ;
        Val_domain detval (espace.get_domain(dd)) ;
        detval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              + (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd)
              + (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              - (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)
              - (*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(1,1)(dd)
              - (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)  ;
 
        // Compo 1 1
        cmpval = (*syst->cst[place]->val_t)(2,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              -(*syst->cst[place]->val_t)(2,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd) ;
        val.set_domain(dd) = cmpval /detval ;
        res[0] = new Term_eq (dd, val) ;
          
        // Compo 1 2
        cmpval = (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              -(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(3,3)(dd) ;
        val.set_domain(dd) = cmpval /detval;
        res[1] = new Term_eq (dd, val) ;
          
        // Compo 1 3
        cmpval = (*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(2,3)(dd)
              -(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(2,2)(dd) ;
        val.set_domain(dd) = cmpval /detval;
        res[2] = new Term_eq (dd, val) ;
        
        // Compo 2 2
        cmpval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(3,3)(dd)
              -(*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,3)(dd) ;
        val.set_domain(dd) = cmpval/detval ;
        res[3] = new Term_eq (dd, val) ;
        
        // Compo 2 3
        cmpval = (*syst->cst[place]->val_t)(1,3)(dd)*(*syst->cst[place]->val_t)(1,2)(dd)
              -(*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,3)(dd) ;
        val.set_domain(dd) = cmpval /detval;
        res[4] = new Term_eq (dd, val) ;
        
          // Compo 3 3
        cmpval = (*syst->cst[place]->val_t)(1,1)(dd)*(*syst->cst[place]->val_t)(2,2)(dd)
              -(*syst->cst[place]->val_t)(1,2)(dd)*(*syst->cst[place]->val_t)(1,2)(dd) ;
        val.set_domain(dd) = cmpval /detval;
        res[5] = new Term_eq (dd, val) ;
        
        // Value field :
        Metric_tensor resval (espace, CON, basis) ;
        resval.set(1,1) = res[0]->get_val_t() ;
        resval.set(1,2) = res[1]->get_val_t() ;
        resval.set(1,3) = res[2]->get_val_t() ;
        resval.set(2,2) = res[3]->get_val_t() ;
        resval.set(2,3) = res[4]->get_val_t() ;
        resval.set(3,3) = res[5]->get_val_t() ;
        
        Metric_tensor zero (espace, CON, basis) ;
        for (int i=1 ; i<=3 ; i++)
          for (int j=i ; j<=3 ; j++)
            zero.set(i,j) = 0 ;
        
        if (p_met_con[dd]==0x0)
            p_met_con[dd] = new Term_eq(dd, resval, zero) ;
        else
            *p_met_con[dd] = Term_eq(dd, resval, zero) ;
        for (int i=0 ; i<p_met->get_n_comp() ; i++)
            delete res [i] ;
        delete [] res ;
    }
}}